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This patch fixes raciness and thread safety issues in
NestedMessagePumpAndroid by reimplementing it on top of the regular
MessagePumpAndroid. This allows us to remove the complicated 100ms
timeslicing logic between Java and C++ tasks and just share the
underlying Looper directly.

Bug: 872269
Change-Id: Id5f5e42f2dac6f065769d69743d78b1fb04bb916
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2207171Reviewed-by: Michael Thiessen <mthiesse@chromium.org>
Reviewed-by: Andrew Grieve <agrieve@chromium.org>
Commit-Queue: Andrew Grieve <agrieve@chromium.org>
Auto-Submit: Sami Kyöstilä <skyostil@chromium.org>
Cr-Commit-Position: refs/heads/master@{#792326}